Generally, referring to FIG. 9, a quick-engaging hub apparatus comprises a shaft (50) and a hub body (60). The hub body (60) is rotatably mounted on the shaft (50), and a first end of the hub body (60) has a ratchet slot (61). An inner periphery of the ratchet slot (61) comprises a plurality of engaging slots (611), and each two adjacent engaging slots (611) are separated with the same distance. A freewheel body (70) is rotatably mounted on the shaft (50) after the hub body (60), and a first end of the freewheel body (70) facing to the hub body (60) has a wheel body (71) which is mounted on the ratchet slot (61). A plurality of accommodating slots (72) formed on the wheel body (71) are divided into two different formations, a first formation and a second formation, and the first and second formations of the accommodating slots (72) are arranged in alternating pattern around the wheel body (71). Also, separated distances between two adjacent accommodating slots (72) are arranged in two alternating distances which are a width and a width adding a tooth width of the engaging slot (611). Moreover, each of the accommodating slots (72) has an engaging piece (73) and an elastic piece (74) respectively formed at a first end and a second end thereof. Thus, when a bicyclist pedaling forward, the engaging slots (611) on the ratchet slot (61) will engage with the engaging pieces (73) which are the nearest to the engaging slots (611) to achieve a quick-engaging effect.
However, the conventional bicycle hub apparatus is disadvantageous because: (i) the engaging slots (611) on the hub body (60) are engaged with the engaging pieces (73) in a radial engagement manner. Although the radial engagement manner smooths the running action of the bicycle, the engaging pieces (73) might bear an uneven force when shifted on the engaging slots (611). As a result, after a period of use, partial engaging pieces (73) having more abrasions are more likely to be damaged, and thus the engaging pieces (73) needs to be inspected and replaced frequently; and (ii) the number of the engaging slots (611) of the ratchet slot (61) is too small that separated distances between each two engaging slots are increased, resulting in an engaging angle between single engaging piece (73) and single engaging slot (611) being more than 90 degrees. Also, the moving distance for the engaging piece (73) to engage with an engaging slot (611) and the fictional resistance between the engaging pieces (73) and the engaging slots (611) are increased, so that the engaging process consumes a great number of performances, reducing the turns of the bicycle hub apparatus and the sliding distance of the bicycle. Moreover, when a bicyclist starts pedaling again, due to the longer separated distances between the each two engaging slots (611), the engaging pieces (73) might be unable to engage with the engaging slots (611) immediately, resulting in the missing step or the lack of safety. Therefore, there remains a need for a new and improved design for a bicycle hub apparatus to overcome the problems presented above.